1. Field of the Invention
The present invention relates to a method of suppressing coherent noise in seismic data and, more particularly, to a method that utilizes an eigendecomposition of the seismic data.
2. Setting of the Invention
Coherent noise arising from the seismic energy source(s) or other sources is frequently a problem in seismic exploration. This resulting coherent noise can manifest itself in the record of seismic data in a variety of forms, depending on the type of energy source utilized, subsurface structures, rock mechanics, etc. Usually, the coherent noise will appear as an ever increasing zone of impinging bands of off-axis signals that obscure the meaningful reflections. For example, in marine seismic records, this coherent noise can appear as a succession of chevron-shaped bands or possible "back scatter" of the source energy.
Numerous techniques have been developed in the past for improving the signal-to-noise ratio in a seismic data record. One very useful technique involves the use of a principal component analysis method called the Karhunen-Loeve Transform (KLT), which is well known to those skilled in the art, as illustrated by the following articles:
M. J. Greenacre, Theory and Applications of Correspondence Analysis, Academic Press, New York, 1984. PA1 L. L. Scharf and D. W. Tufts, "Rank Reduction for Modeling Stationary Signals," IEEE Trans. on Acoust., Speech, and Signal Proc., Vol. ASSP-35, No. 3, March 1987, pp. 350-355. PA1 C. Hemon and D. Mace, "The Use of the Karhunen-Loeve Transformation in Seismic Data Processing," Geophysical Prospecting, Vol. 26, 1978, pp. 600-626. PA1 I. F. Jones, "Applications of the Karhunen-Loeve Transform in Reflection Seismology," PhD Thesis, Department of Geophysics and Astronomy, University of British Columbia, April 1985.
The Karhunen-Loeve Transform (KLT) has been applied to a variety of seismic data processing problems, including stacking, multiple suppression, and velocity analysis. The KLT was developed as the optimum solution to a mean squared error problem based on the reduced rank modeling of a signal. A discussion of the method of reduced rank modeling of signals and several examples of applications can be found in the Scharf and Tufts article above.
Seismic applications of the KLT typically have involved using a subset of the principal components obtained from the KLT of a seismic data set to reconstruct the data. If the dominant principal components are used to reconstruct the data, the result emphasizes the lateral coherence which characterizes seismic data. Using the subdominant principal components can emphasize detail in data by leaving out the strong lateral information contributed by the dominant principal components. However, the data vectors used in the KLT in the past span only a one-dimensional pattern, such as the elements from a certain number of traces at a fixed sample time.
Since coherent noise in seismic data takes the form of two-dimensional patterns, such as exhibiting spatial and temporal coherency, the use of the one-dimensional KLT has been found to have limitations. Thus, there is a need for a method of suppressing coherent noise in seismic data that utilizes the benefits of the KLT and the two-dimensional coherencies present in the data.